Some of the trust has been lost and the fans now seem to be permanently on the edge. It will take more than a win over a very obliging Bournemouth to win them back round.

A better acid test for Arsenal will come at Chelsea next Sunday when they face Antonio Conte’s defending champions and another defeat will put them back to square one.

They need a fit and firing Sanchez to get them through a tough season and, in fairness, his late cameo performance proved that once on the pitch his will-to-win takes over.

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Danny Welbeck was man-of-the-match, scored twice and set up another for Alexandre Lacazette and his stunning 25-yard effort was the best goal of the game.

But it was still all about Sanchez and that is the reason why Arsenal refused a £60million offer from Manchester City on deadline day. Despite the ugly transfer saga which upset the fans, Sanchez is Arsenal’s main man.

Sanchez now needs games to get himself match fit which is why he could start against Cologne on Thursday night in a mix-and-match team for the Europa League.

Wenger admitted that Sanchez is not fully match fit which is why he put him on the bench but denied claims by Chile’s former Under-20 coach Jose Sulantay that he is “fatter than normal” and “physically out of shape.”

Arsenal boss Wenger revealed he held clear-the-air talks with the forward after he arrived back from international duty with Chile and is convinced that he is in the right frame of mind.

Wenger said: “Yes, I spoke to him. He is focused, he told us he is focused on the Premier League and Europa League. On top of that he had a bad result with Chile against Bolivia, but he came back full of desire and ready to play.

“He was not completely physically ready to play three games in a week - and for Chile he was not completely ready.

“He is not fat. His fat percentage is under 10. You know how it is, when you do not win, people will find problems.”

Sanchez back at the heart of the action (Image: CameraSport)

Sanchez saw a move to Manchester City fall through (Image: AFP/Getty Images)

It was backed up by Arsenal keeper Petr Cech and clearly the rest of the dressing room have also sought assurances from Sanchez over his attitude, particularly after that devastating four goal thrashing at Liverpool.

Cech said: “I spoke with Alexis and he wants to win. Some people say, ‘he does this, he does that’. But I think he’s a guy who plays with all of his passion and all of his heart. You could see that in his performance.

“He knew he came late back, the manager opted not to risk him, put him on the bench so he was ready to come on. He came on and you could see he put a shift in.”

It was an impressive performance by Arsenal in that you could sense a determination to respond after the Liverpool defeat. They were sharp, tenacious and determined in every department.

It was just the tonic Arsenal needed at the Emirates. The fans do seem to be louder in defeat than they are in victory and yet Wenger will have taken heart from the rousing chants of “Arsenal” during the second half.

The Gunners made light work of Bournemouth (Image: PA)

But Arsenal now face the Europa League for the first time on Thursday. The big Champions League nights are gone for a season at least and Wenger is considering ringing the changes. Jack Wilshere could return and Mathieu Debuchy may even reappear.

But Wenger admitted they cannot afford to even contemplate taking any home game lightly because the way the mood changes so quickly.

Wenger added: “Thursday to Sunday morning is short so yes - I have to think about that (rotation). But we have to win at home and you know how it is when you don’t win at home.

“At least it is a new experience for us. We will take it seriously but the priority is to focus on the Premier League and combining the two and then in December we will see, but at least we want to qualify for the next round.”